﻿ Intepreting results: Mixed model two-way

# Intepreting results: mixed effects model two-way

## P values

When interpreting the results of fitting a mixed model, interpreting the P values is the same as two-way ANOVA. So read the general page on interpreting two-way ANOVA results first. Also read the general page on the assumption of sphericity, and assessing violations of that assumption with epsilon.

## Random effects SD and variance

The mixed effects model treats the different subjects (participants, litters, etc) as a random variable. The residual random variation is also random. The effect of all random variables is quantified with its variation. Prism presents the variation as both a SD and a variance (which is the SD squared). You, or more likely your statistical consultant, may be interested in these values to understand the relative variation among subjects responses (the subject variance) and within the repeated responses from the same subject (the residual variance). compare with other programs.

## Was the matching effective?

A repeated-measures experimental design can be very powerful, as it controls for random factors that cause  or unmeasured variability between subjects. If the matching is effective, the repeated-measures test will yield a smaller P value than an ordinary ANOVA. The repeated-measures test is more powerful because it separates between-subject variability from within-subject variability. If the pairing is ineffective, however, the repeated-measures test can be less powerful because it has fewer degrees of freedom.

Prism tests whether the matching was effective and reports a P value. This P value comes from a chi-square statistic that is computed by comparing the fit of the full mixed effects model to a simpler model without accounting for repeated measures. If this P value is low, you can conclude that the matching was effective. If the P value is high, you can conclude that the matching was not effective and should reconsider your experimental design for your next study.

## Goodness of fit

Prism expresses the goodness-of-fit in a few ways. These will only be meaningful to someone who understand mixed effects models deeply. Most scientists will ignore these results or not check the option so they never get reported. But some journals may ask you to report at least one measure of goodness of fit.

## If you don't accept the assumption of sphericity

If you checked the option to not accept the assumption of sphericity, Prism does two things differently.

It applies the correction of Geisser and Greenhouse. You'll see smaller degrees of freedom, which usually are not integers. The corresponding P value is higher than it would have been without that correction.

It reports the value of epsilon, which is a measure of how badly the data violate the assumption of sphericity.

## Multiple comparisons tests and analysis checklist

Before interpreting the results, review the analysis checklist.